MGMT 675
AI-Assisted Financial Analysis

Autoregression

Overview

• We start the forecasting part of the course.
• Forecast returns, interest rates, oil price, cash flows, …
• Possible models:
  • ARIMA (autoregressive integrated moving average)
  • exponential smoothing
  • neural networks

Autocorrelations

• The correlation of a variable with its lagged value
• First-order autocorrelation \(=\text{corr}(x_t, x_{t+1})\)
• \(p\)–th order autocorrelation \(=\text{corr}(x_t, x_{t+p})\)
  • E.g., seasonality in monthly data captured with \(p=12\) or in quarterly data with \(p=4\).

Autocorrelation of HML

• Ask Julius to use pandas-datareader to download the monthly Fama-French factors from Ken French’s data library.
• Ask Julius to produce a plot of the autocorrelation function (acf) for HML.

Autoregressions

• An autoregression is a regression of a variable on its own lags: \[x_t = \alpha + \beta_1x_{t-1} + \cdots + \beta_px_{t-p} + \varepsilon_t\]
• Ask Julius to fit an AR(1) for HML.
• Ask Julius to use the AR(1) model to forecast HML for the next 12 months and to plot the last 2 years and the forecasts.

More examples

Ask Julius to plot the ACF, fit an AR model, and forecast the following:

• Percent change in crude price: Ask Julius to use pandas-datareader to download crude oil prices starting in 1980 from FRED, to downsample to end-of-month, and to compute percent changes.

• Change in Treasury yields: Ask Julius to use pandas-datareader to download 10-year Treasury yields starting in 1980 from FRED, to downsample to monthly, and to compute changes.